Problem: $f(x) = 2x^{2}-2$ What is the range of $f(x)$ ?
Consider the range of $2x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $2$ doesn't change the range. To get $2x^{2}-2$, we subtract $2$. So the range becomes: $\{\, y \mid y ≥ -2 \,\}$.